SOLUTION: How many quarts of pure antifreeze must be added to 5 quarts of a 30% antifreeze solution to obtain a 50% antifreeze solution

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Question 1184009: How many quarts of pure antifreeze must be added to 5 quarts of a 30% antifreeze solution to obtain a 50% antifreeze solution
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


A classic formal algebraic solution would go something like this....

You are mixing 5 quarts that is 30% antifreeze and x quarts that are 100% antifreeze to get (5+x) quarts that is 50% antifreeze:






ANSWER: 2 quarts

An informal method that will give you the answer within 15 seconds if you understand it....

(1) Look at the three percentages 30, 50, and 100 on a number line and observe/calculate that 50 is 2/7 of the way from 30 to 100. (30 to 100 is a difference of 70; 30 to 50 is a difference of 20; 20/70 = 2/7.)
(2)That means 2/7 of the mixture is the 100% antifreeze that you are adding.
(3) So the 5 quarts you started with is 5/7 of the mixture; that means 2/7 of the mixture is 2 quarts.

ANSWER: 2 quarts
Answer by ikleyn(52787)   (Show Source): You can put this solution on YOUR website!
.
How many quarts of pure antifreeze must be added to 5 quarts of a 30% antifreeze solution
to obtain a 50% antifreeze solution
~~~~~~~~~~~~~~~~~~~~~


            In my previous post,  I gave a detailed description of the solution procedure to a  TWIN  problem in word form.
            THEREFORE,  I will omit here all the words and will present the solution in short form. 


The basic equation is


     = 0.5


    x + 0.3*5 = 0.5*(x+5)

    x + 1.5  = 0.5x + 2.5

    x - 0.5x  = 2.5 - 1.5

      0.5x    = 1.0

         x    =  = 2.


ANSWER.  2 quarts of the pure antifreeze must be added.


CHECK.    =  =  = 0.5 = 50%    ( ! correct concentration ! )

Solved.



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